Encyclopedia Removal Grid

A library shelf is an `n × m` grid of encyclopedias, each labeled by author. Selecting one encyclopedia removes all books by the same author in its row and column; minimize selections to clear the shelf. Requirements Input: an n × m grid. Each cell contains an author id from 1 to k. Operation: select a cell (i, j). Every encyclopedia by the same author in row i or column j is removed along with the selected one. Output: the minimum number of selected cells needed to remove every encyclopedia. Notes Full constraints were not included, so clarify n, m, and k before choosing between brute force, matching / cover formulations, or per-author decomposition. The operation is author-specific: selecting author a in a row/column does not remove different-author cells in that row/column. The prompt was paired with Process Starvation Time as the harder 2026 Engineering OA question. Preparation Model a single author as a bipartite row-column incidence graph and reason about what a selected occupied cell covers. Prepare a fallback brute-force / backtracking explanation for small grids, then discuss how constraints would change the approach.